The bad side to a multicultural society is that it diminishes the country as its culture is diluted. England, for example, is very multicultural but traditional English places has been mixed with the foreign takeaway.
The countries may also change for tourists e.g. traditional dances will be performed to tourists and edited to suit tourists, losing the dances purity and original meaning.
Believing in certain values and traditions when you are in a country which has the opposite ideas, can sometimes cause conflict. For example, if a group of people immigrated to a country and decided the elders of the group should decide punishments for crimes done by people in the group and not letting the police get involved.